Material fluid permeability is an essential quality measurement in a variety of industries including textiles and papermaking. Permeability in itself is related to the porosity, density, and thickness of a material. Consistency of these material properties over time is required within a process as an indication of the quality. The purpose of permeability measurement is to accurately indicate the quality and consistency of a material product.
Historically, airflow permeability measurement devices have followed one of two basic genres: series or bridge. The bridge method, exemplified by Gurley Precision Instruments Co. [of Troy, N.Y.] Permeometer, compares pressure drops across two streams with a single vacuum source. One flow stream passes through a variable valve, comparator chamber, and fixed orifice to the reservoir, while the second passes through the unknown sample material, test chamber, and variable micrometer orifice into the reservoir. Orifices are varied until the pressure drop across the variable orifice is fixed at 0.5 inches of water and the pressures in both the test chamber and comparator chamber are equal, thus the pressure drop across the unknown sample is also 0.5 inches of water.
Among the many assumptions necessary for this measurement is the standard environment. Conditions such as temperature or relative humidity affect various components of permeability measurements. In 1856, Henry Darcy published an equation for the basic relationship of flow through porous media. He discovered that discharge varies directly with head loss over distance, for small discharges. Although recent modifications have been made to the coefficients, the relation has remained the same. Darcy's equation is:       h    f    =      c    ⁢                   ⁢                  μ        ⁢                                   ⁢        VL                    γ        ⁢                                   ⁢                  d          2                    (Albertson, et al. Fluid Mechanics, p.211-212). Where hf is head loss, V is the mean velocity of flow, μ is the fluid absolute viscosity, γ is the fluid specific weight, d is the characteristic grain diameter of the porous material, and c is the dimensionless coefficient which describes the porous media by including the size and distribution of grains, the porosity, and the orientation and arrangement of the grains. This is referred to as the coefficient of permeability and is equal to the pressure drop over specific weight. Note that the new flow coefficient KD if d2 over coefficient c. Rewriting for volumetric flow equal to bulk velocity times area gives:   Q  =            A      ⁢                           ⁢      Δ      ⁢                           ⁢              PK        D                    L      ⁢                           ⁢      μ      
It should be noted that density does not enter into the equation of laminar flow through a porous material. For laminar flow, the forces of inertia, which depend on density, are negligible and the forces of viscosity are in complete control. Since viscosity is a fluid property, it does not change with pressure or location within the flow. Flow through a porous material can be characterized by low velocity, high-pressure drop, and very small pore diameter, so the conditions for laminar flow, such as a small Reynolds number, is consistent.
Normalizing the flow constant per unit length, this dependence on viscosity is an inherent dependence on temperature. According to the Handbook of Chemistry and Physics, for air, absolute viscosity can be expressed solely as a known function of temperature, linear in the region from 20 to 60 degrees Celsius.   Q  =            A      ⁢                           ⁢      Δ      ⁢                           ⁢              PK        N              μ  
However, air not only flows through this permeable membrane, but also various orifices. Flow through a fixed orifice is generally expressed in the Bernoulli corrected form asV=(2gh)½(Binder, Fluid Mechanics, p. 99). Where h is a head loss, commonly replaced by ΔP over γ, and γ is the specific weight or fluid density times gravitational constant. Expressed in terms of volumetric flow rate,   Q  =            KA      ⁡              (                              2            ⁢            Δ            ⁢                                                   ⁢            P                    ρ                )                    1      /      2      Where K is a new flow constant, A is the orifice area and ρ is the fluid density. Coefficient K is required because the cross-sectional are A is inconsistent in the flow on fluid through an orifice. Density, however, is much more difficult to specify than absolute viscosity. It requires knowledge of atmospheric pressure, vapor pressure, relative humidity, temperature and precise compressibility. Flow through an orifice is one of the oldest, yet most reliable, methods of measuring and controlling the flow of fluids (Binder), which most likely explains the historical use in permeability measuring devices, however the limitation is in the accurate specification of fluid density.
A permeameter sold by Frazier, Inc. [of Hagerstown, Md.] benchmarks the series method. The device draws a variable suction across the permeable membrane and a fixed but alterable orifice. Pressure drop across the porous sheet-like material is held to a standard, while the pressure drop across the fixed orifice is measured and compared with calibrated results. Once again, problems arise with changes in atmosphere. Changes in temperature, pressure, humidity, et cetera, between the conditions at calibration and the conditions at measurement will cause error in results.
The simple series device above is governed by Darcy's Law and flow through an orifice. Equating, the normalized permeability constant for a particular sample test section may then be determined as follows       K    N    =                              K          orifice                ⁢                  A          orifice                ⁢                              μ            ⁡                          (                                                2                  ⁢                  Δ                  ⁢                                                                           ⁢                                      P                    orifice                                                  ρ                            )                                            1            /            2                                                A          membrane                ⁢        Δ        ⁢                                   ⁢                  P          membrane                      .  Solving and combining with Darcy's Law at standardized conditions yields the industrial standard permeability. The result is, once again, dependent upon temperature, through viscosity (μ) and further atmospheric conditions such as humidity, through density (ρ).
Permeability measurement has been a necessary quality control measurement in industry, including textile and paper industries. The measurement issued as a fault detection platform across a web product span and between successive products or webs. The main goal is to detect errors or inconsistencies in a product or web, indicating process malfunction or necessary web replacement due to use. For example, U.S. Pat. No. 4,495,796 uses an ad hoc permeability measurement as mechanical error detection following a cigarette paper perforation device. U.S. Pat. No. 5,436,971 describes a device for measuring air permeability across a textile to find manufactured, woven inconsistencies.
Single chamber designs have been developed as well, Such as described in U.S. Pat. Nos. 4,756,183 and 4,991,425, both of which are single chamber devices that ignore the change in permeability due to temperature change.
Most devices patented to this point ignore flow changes due to atmospheric conditions. These devices assume that all measurements are taken at standard conditions, which though desirable, is neither consistently practiced nor universally practical for industrial use.
U.S. Pat. No. 4,649,738 takes atmospheric changes into consideration while integrating high-speed permeability measurements in an industrial process. The sample focused on is cotton at various stages of the cotton ginning process. The device measures differentially over a measurement stream and reference stream. The device does not, however, measure across an entire sample, use a reference sample, or provide an accuracy level that is needed in most applications. The device is also specific to the measurement of a continuous flow of cotton, and sheet-like materials cannot be measured using the present cofiguration.
It is clear that changes in atmospheric conditions will cause alteration of standard expected flows, in differing amounts between an orifice and a permeable membrane. Thus, measured pressure drop for a single material will change as atmospheric conditions change. Removal of the dependence of these conditions on the measurement of permeability will therefore vastly improve the accuracy of measurement.
It is an object of the invention is to provide a method and device of measuring differential permeability that eliminates environmental factors and measures permeability accurately by measuring the differential pressure drop across a fluid flow after flowing through a test sample and the fluid flow after flowing through a reference sample.
It is another object of this invention to increase the limits of permeability measurement accuracy.
It is another object of this invention to introduce the theory of differential measurement across two samples to determine the permeability of a porous material.
It is another object of this invention to eliminate variations in results of permeability measurements due to a changing environment.
It is another object of this invention to increase permeability measurement accuracy by changing the required range of gauge measurement.